Description
Let X be a hypersurface. On one hand, in the context of hyper-surface deformation theory, X can be deformed locally to a smooth space F_X (the Milnor-Le fiber of X). On the other hand, thanks to the theory of resolution of singularities formulated by Hironaka, X can be modified to a smooth space X', without modifying its regular part. Now, take a mapping f : X^n → M^{n+1}. In the context of deformation theory (Thom-Mather theory), if X is smooth then f can be perturbed locally to a (topologically) stable one f_t. On the other hand, a theory similar to the resolution of singularities, but for mapping, does not yet exist. Hence our aim is to start formulating the so call Resolution of instabilities of a mapping which returns a stable map f' replacing the unstable points of f with stable ones. In particular, we are interested in defining a good resolution of instability that provides topological information through the resolution graph
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Meeting ID: 865 7014 5006
Passcode: 287154